médian

Médian is a term used in French to denote the middle or midline in various fields. As an adjective, it describes something related to the middle, such as a median plane or a median nerve. In mathematics, it appears in two related senses: geometry (the median of a triangle) and statistics (the median as a measure of central tendency.

In geometry, the median of a triangle is the segment that connects a vertex with the midpoint of the opposite side. Each triangle has three medians, which intersect at a single point called the centroid. The centroid divides each median in a 2:1 ratio, with the longer portion lying between the vertex and the centroid. Medians are fundamental in proving many geometric properties and in understanding triangle balance.

In statistics, the médian is the value that separates a data set into two equal halves when the data are ordered. If the number of observations n is odd, the médian is the middle value; if n is even, it is the average of the two central values. The médian is a robust measure of central tendency, less sensitive to extreme outliers than the arithmetic mean.

In anatomy and anatomy-related geometry, the term médian appears in phrases such as plan médian (midline plane) and nerf médian (median nerve), indicating structures located along or near the body's midline. The concept of médian thus conveys a sense of centrality across diverse disciplines.

Etymology traces to Latin medius, meaning middle.